Question: Solve for $x$ : $4\sqrt{x} + 7 = 10\sqrt{x} + 6$
Solution: Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} + 7) - 4\sqrt{x} = (10\sqrt{x} + 6) - 4\sqrt{x}$ $7 = 6\sqrt{x} + 6$ Subtract $6$ from both sides: $7 - 6 = (6\sqrt{x} + 6) - 6$ $1 = 6\sqrt{x}$ Divide both sides by $6$ $\frac{1}{6} = \frac{6\sqrt{x}}{6}$ Simplify. $\dfrac{1}{6} = \sqrt{x}$ Square both sides. $\dfrac{1}{6} \cdot \dfrac{1}{6} = \sqrt{x} \cdot \sqrt{x}$ $x = \dfrac{1}{36}$